Nonparametric Time-Varying Coefficient Panel Data Models with Fixed Effects
Nonparametric Time-Varying Coefficient Panel Data Models with Fixed Effects
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DOI：
10.2139/ssrn.1677767
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发表时间：
2010-09
期刊：
影响因子：
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通讯作者：
Jia Chen;Degui Li;Jiti Gao
中科院分区：
文献类型：
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作者：
Jia Chen;Degui Li;Jiti Gao
本文致力于开发一种具有固定效应的非参数时变系数模型，以表征非线性面板数据分析中的非平稳性和趋势现象。我们开发了两种方法来估计趋势函数和系数函数，而不采用一阶差分来消除固定效应。第一个方法通过取横截面平均值来消除固定效应，然后使用非参数局部线性方法来估计趋势函数和系数函数。该方法的渐近理论表明，虽然趋势函数和系数函数的估计值是一致的，但系数函数的估计值的最优收敛速度慢于同样具有最优收敛速度的趋势函数的估计收敛速度。为了更有效地估计系数函数，我们提出了一种合并局部线性虚拟变量方法。这是由参数面板数据分析中提出的最小二乘虚拟变量方法推动的。该方法通过扣除每个个体的跨时间平均值的平滑版本来消除固定效应。它以最佳收敛速度估计趋势函数和系数函数。当 T 趋于无穷大并且 N 固定或者 T 和 N 都趋于无穷大时，两个估计值的渐近分布成立。提供仿真结果来说明所提出的估计方法的有限样本行为。
This paper is concerned with developing a nonparametric time-varying coefficient model with fixed effects to characterize nonstationarity and trending phenomenon in nonlinear panel data analysis. We develop two methods to estimate the trend function and the coefficient function without taking the first difference to eliminate the fixed effects. The first one eliminates the fixed effects by taking cross-sectional averages, and then uses a nonparametric local linear approach to estimate the trend function and the coefficient function. The asymptotic theory for this approach reveals that although the estimates of both the trend function and the coefficient function are consistent, the estimate of the coefficient function has an optimal rate of convergence that is slower than that of the trend function, which also has an optimal rate of convergence. To estimate the coefficient function more efficiently, we propose a pooled local linear dummy variable approach. This is motivated by a least squares dummy variable method proposed in parametric panel data analysis. This method removes the fixed effects by deducting a smoothed version of cross-time average from each individual. It estimates the trend function and the coefficient function with an optimal rate of convergence. The asymptotic distributions of both of the estimates are established when T tends to infinity and N is fixed or both T and N tend to infinity. Simulation results are provided to illustrate the finite sample behavior of the proposed estimation methods.